Acts like battery is almost dead but it isn't.

Hi Mark, I would agree with your diagnostics. If you have replaced the battery already before replacing the starter motor make sure all the connection including the negative connections are clean and making good contact. Once that has been done and still no improvement go for the starter motor. Regards John

You need a motor. If it overheated and stalled as a result than you cooked the engine.

I’m happy to assist further over the phone at https://www.6ya.com/expert/jeremy_d728a59f986299fa

If the car doesn't start with a jump you might have a bad alternator. The alternator supplies voltage to the car once the engine is running. If the battery is dead, and the alternator isn't putting out sufficient voltage, the engine cannot run. Then again sometimes a car with an extremely dead or internally shorted battery WON'T start with a jump. Replace the battery and try again.

could be a starter relay

you could just have dead cell in the battery which isn't getting enough amps to the starter,, have the battery LOAD checked,, that will tell you if the battery is actually good, just because it registers 12 volts isn't necessarily an indication that the required amps are present.

This is an indication that you have a bad or loose connection at the battery. Check the cable ends on the battery and clean them of any green looking stuff. Make sure all connection are tight at the battery.

your charging system isn't working, if you replaced the battery and it worked for a few days, then its not being re charged after starting, I'm assuming you cleaned and tightened all the battery post connections when you installed the new battery , if not do so ,, charge the battery from an outside source, once you know its fully charged,, use a meter, and start the car ,, check the voltages at the battery posts,, you should be getting a reading of 13.5-14.5 volts, if not your alternator isn't charging the battery

dead battery, charge it.

This sounds like there is a dead spot in your starter. The easiest way to resolve this issue is to replace your starter. Many times, if you take a lot of short-distance trips over the life of your car, the wiring inside the starter itself will wear (short trips means starting it more often, causing a lot of wear over time). Then the inner wiring of the starter wears too much, it forms a "dead spot" -- when the starter is stopped at a very specific spot i will not form the magnetic force needed to torn the starter motor. This is a common issue which can be dealt with for a time if you have to save the money to replace the starter. Tapping the starter, or arcing it with a screwdriver makes the inner workings of the starter jump a little, allowing it to move out of the dead spot and kick over as normal, but it is only a temporary fix. Unless you refurbish electronics for a living, it is very unlikely that you will be able to repair the starter on your own, and such a repair takes some time, so you are better off to replace it than try to repair the starter itself.
As long as the starter does not happen to stop in the dead spot, it will work as normal ... but in time the dead spot will spread, causing the issue to worsen. You can keep forcing it to turn with the two tricks you used until you have had the opportunity to earn the money to replace the starter (or until you have a day off to get the repairs done) .. but over time this can cause more damage to other parts of the car, so I recommend replacing the starter as soon as you can.

Is it one click or multiple clicks. If it's multiple clicks, it sounds like a dead battery. Voltage isn't always an indicator of a good battery, you need to have enough cranking amps to be able to start an engine also. If you have dash lights and it only clicks once, you could have a bad starter. An easy way to check this is to try and jump start the vehicle. If it starts up with a jump start, you need a new battery. If it still doesn't start up and it just clicks, you probably need a new starter.

Good Luck!
~Brandon